Problem: The following line passes through point $(-1, -7)$ : $y = \dfrac{9}{4} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-1, -7)$ into the equation gives: $-7 = \dfrac{9}{4} \cdot -1 + b$ $-7 = -\dfrac{9}{4} + b$ $b = -7 + \dfrac{9}{4}$ $b = -\dfrac{19}{4}$ Plugging in $-\dfrac{19}{4}$ for $b$, we get $y = \dfrac{9}{4} x - \dfrac{19}{4}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-1, -7)$